Analysis of half-spin particle motion in Reissner–Nordström and Schwarzschild fields by the method of effective potentials

Abstract

The paper presents an analysis of effective potentials of Dirac equations in Schwarzschild and Reissner–Nordström fields. It is shown that in the majority of the explored cases the condition of a particle “fall” to the corresponding event horizons is fulfilled. An exception is one of the solutions with a normalizable wave functions for the Reissner–Nordström extreme field, for which the existence of a stationary bound state of a half-spin particles is possible inside the event horizon.